Two-Qubit Gates on Tunable Transmons
Frequency tunability lets transmons realize controlled-phase and exchange gates by moving qubits into resonance with each other or with a coupler.
Tuning Into Interaction
When a qubit's frequency can be moved with flux, entangling gates become a matter of steering levels into and out of resonance. Two families dominate: the controlled-phase (CZ) gate, which uses an avoided crossing involving a non-computational state, and exchange-type gates such as iSWAP, which use resonance between the single-excitation levels of two qubits.
The Adiabatic and Diabatic CZ
In the CZ approach one qubit is tuned so that its two-excitation state approaches the state where the neighbor holds an excitation and the qubit is in its second excited level. The avoided crossing between these levels imparts a state-dependent phase. Driving the tuning slowly, adiabatically, accumulates a conditional phase; driving it fast, diabatically, uses a rapid excursion and return. Both aim to accumulate a net conditional phase of pi while returning all population to the computational subspace.
- Adiabatic CZ: smooth flux pulse, robust to some timing error, slower.
- Diabatic CZ: fast flux excursion, shorter gate, tighter timing tolerance.
- Net-zero flux pulses reduce long-timescale distortion and heating in the flux line.
Exchange Gates
When two qubits are brought to the same frequency, their coupling swaps a single excitation between them at the coupling rate. Holding resonance for a full swap gives iSWAP; a half swap gives the entangling square-root-of-iSWAP. Parametric variants modulate the flux at the difference frequency of the two qubits so they exchange without static resonance, keeping each qubit near its sweet spot for most of the gate.
Practical Concerns
Every tuned gate must contend with flux-pulse distortion, leakage into higher levels, and the dephasing incurred while off the sweet spot. Flux pulses are pre-distorted to compensate the control line's frequency response, and pulse shapes are optimized to suppress leakage. The reward is fast, high-fidelity entanglement without any need for the frequency planning that constrains fixed-frequency devices.
These gates are the reason tunable couplers and asymmetric SQUIDs appear so often in modern architectures.